Personally, I don't really care about the details of the setting in any of the Doom games. As long as the game is still set in the near future, with lots of guns and monsters, I'm happy enough.
What made the original Doom really great was the clever level design, unique monsters, and the fast, speed-based gameplay. In modern shooters, you spend a lot of time with the infamous duck-and-cover mechanic; you are made to feel powerful because you can inhale bullets, duck, regenerate, and inhale bullets again. Anybody can play a game like that, but it's just not very fun.
But in Doom, you have to do a lot of moving around. The monsters in Doom are very, very stupid, but because of their large numbers you are forced to find a way to weave around them and perform crowd control as best you can. Combine this with the unique, abstract level design, and you are forced to work your way around tons of weird, moving obstacles, all the while fighting off monsters with your futuristic guns and weapons.
Doom3 isn't very fun because it abandons this run-and-gun gameplay to a slower paced game primarily based on graphics and detail. The levels are cramped, monotonous, and you never run into more than a few monsters at a time. Doom3 even makes use of the duck-and-cover mechanic when you fight the zombies, who like to take cover behind walls and boxes and shoot at you every few seconds. Doom3 is only "Doom" in the sense that it had nice graphics for its time and is based on the whole idea of Demons vs. Space Marines.
For Doom4, I hope they return to the fast paced, action oriented gameplay originally found in Doom. The AI should only be at the bare minimum, there should be hordes of monsters, and the level design should be abstract but interesting. The weapons should have the proper sounds and punch, and the music and theme should be stylish and unique.
As a final random note, I don't know if any of you guys have ever played Crimsonland, but it's a top-down shooter where you're a space trooper of some kind and you have to fight off swarms of aliens and zombies. It's a lot of fun, for a reason: the game is a lot like Doom in that you have to spend a lot of time running around, dodging enemies, and unloading your weapons into the closer enemies as fast as you can. The game even has catchy theme music and good sound effects.